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Show that the straight lines whose direction cosines are given by the equations `a l+b m+c n=0` and `u l^2+z m^2=v n^2+w n^2=0` are parallel or perpendicular as `(a^2)/u+(b^2)/v+(c^2)/w=0ora^2(v+w)+b^2(w+u)+c^2(u+v)=0.`

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RD SHARMA ENGLISH-DIRECTION COSINES AND DIRECTION RATIOS-All Questions
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  2. A line makes angles alpha,""""beta,""""gamma and delta with the ...

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  3. Show that the straight lines whose direction cosines are given by th...

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  4. If a variable line in two adjacent positions has direction cosins l ...

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  5. If the edges of a rectangular parallelepiped are a ,b ,c prove that th...

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  6. If three mutually perpendicular lines have direction cosines (l1,m1,n...

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  7. Find the direction cosines of the sides of the triangle whose verti...

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  8. Prove that the straight lines whose direction cosines are given by ...

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  9. The x-coordinates of a point on t line joining the points Q(2,2,1)a...

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  10. Given that P(3,2,-4),Q(5,4,-6)a n dR(9,8,-10) are collinear. Find the ...

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  11. Find the coordinates of the foot of the perpendicular drawn from th...

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  12. Find the angle between the vectors with direction ratios proportion...

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  13. Determine the point in XY-plane which is equidistant from thee poin...

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  14. Find the angle between the lines whose direction cosines are given b...

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  15. Find the distance between the points A and B with position vectors hat...

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  16. Find the locus of the point which is equidistant from the points A(0...

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  17. Find the distance between the points P(-2,4,1) and Q(1,2,5).

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  18. Prove by using distance formula that the points P(1,2,3),Q(-1,-1,-1)a ...

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  19. Show that the points A(0,1,2),B(2,-1,3)a n dC(1,-3,1) are vertices of ...

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  20. Find the coordinates of a point equidistant from the four points O(...

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